How to set object to world origin?
You press Shift+s to set your Cursor "to origin", then you can press once again Shift+s and select "to Cursor" which will snap your selected object to the cursor, which you previously set back to origin.

To make new objects aligned to the center x, y and z axis, which is essentially at origin, just set the cursor back to origin. Thus new objects will be created there.

For completeness sake, setting the cursor to origin can also be done with the Shift+c shortcut, which avoids the pie-menu.